Analysing and Interpreting the Yield Curve, 2nd Edition

CHAPTER 5Interest Rate Models I

In Chapter 4 we introduced the concept of stochastic processes. Most, but not all, interest rate models are essentially a description of the short‐term rate in terms of a stochastic process. Recent literature has tended to categorise models into one of six different types, but for our purposes we can generalise them into two types. Thus, we introduce some of the main models, according to their categorisation as equilibrium or arbitrage‐free models. This chapter looks at the earlier models, including the first ever term structure model presented by Vasicek in 1977. Chapter 6 considers what have been termed “whole yield curve” models, or the Heath–Jarrow–Morton family, while Part III reviews considerations in modelling the yield curve.

INTEREST RATE MODELS

An interest rate model provides a description of the dynamic process by which rates change over time, in terms of a statistical construct, as well as a means by which interest rate derivatives such as options can be priced. It is often the practical implementation of the model that dictates which type is used, rather than mathematical neatness or more realistic assumptions. An excellent categorization is given in James and Webber (2000) who list models as being one of the following types:

• the traditional one‐, two‐ and multi‐factor equilibrium models, known as affine term structure models (see James and Webber (2000) or Duffie (1996, p. 136)). These include Gaussian affine models such as Vasicek, ...